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    LCM for 20, 24 and 45

    "Least Common Multiple of 3 Numbers" Calculator
    Least Common Multiple of
    ,
    and

    What's the Least Common Multiple (LCM) of 20, 24 and 45?

    Answer

    LCM of 20, 24 and 45 is
    360

    (Three hundred sixty)

    360 is the smallest positive integer that 20, 24 and 45 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 20, 24 and 45 by Prime Factorization

    Split all three numbers into prime factors, then take every prime that shows up in at least one of them, each raised to the highest power it reaches there. Multiplying those highest powers gives the least common multiple:

    All Prime Factors of 20: 2 × 2 × 5 (exponent form: 22 × 5)

    All Prime Factors of 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

    All Prime Factors of 45: 3 × 3 × 5 (exponent form: 32 × 5)

    Prime factor202445Highest power
    22223—23
    3—33232
    55—55

    LCM = 23 × 32 × 5 = 360

    Checking the LCM of 20, 24 and 45 Two Numbers at a Time

    The least common multiple is associative, so three numbers can be handled as two pairs: first the LCM of the first two, then the LCM of that value and the third. Each pair goes through the two-number formula, which uses the greatest common divisor:

    LCM(a, b) = (a × b) ÷ GCD(a, b)

    LCM(20, 24) = (20 × 24) ÷ 4 = 480 ÷ 4 = 120

    LCM(120, 45) = (120 × 45) ÷ 15 = 5,400 ÷ 15 = 360

    LCM(20, 24, 45) = 360

    The pairs may be taken in any order — 24 and 45 first, then 20 — and the answer is the same 360. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 20, 24 and 45?. The LCM of 20, 24 and 45 is 360 — the smallest number all three divide with no remainder. Step-by-step solution for three numbers.
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    LCM Table

    Number 1Number 2Number 3LCM
    202430120
    2024313,720
    202432480
    2024331,320
    2024342,040
    202435840
    202436360
    2024374,440
    2024382,280
    2024391,560
    202440120
    2024414,920
    202442840
    2024435,160
    2024441,320
    202445360
    2024462,760
    2024475,640
    202448240
    2024495,880
    202450600
    2024512,040
    2024521,560
    2024536,360
    2024541,080
    2024551,320
    202456840
    2024572,280
    2024583,480
    2024597,080

    About "Least Common Multiple of 3 Numbers" Calculator

    This calculator finds the Least Common Multiple (LCM) of three numbers at once, without doing it in two passes. For example, it can help you find out what's the Least Common Multiple (LCM) of 20, 24 and 45? (The answer is: 360). Enter the first number (e.g. '20'), the second (e.g. '24') and the third (e.g. '45'), then hit the 'Calculate' button.
    The Least Common Multiple of three numbers is the smallest positive integer that all three of them divide without a remainder
    "Least Common Multiple of 3 Numbers" Calculator
    Least Common Multiple of
    ,
    and

    FAQ

    What's the Least Common Multiple (LCM) of 20, 24 and 45?

    LCM of 20, 24 and 45 is 360

    How to find the LCM of 20, 24 and 45 by prime factorization?

    Take every prime that appears in 20, 24 and 45 to the highest power it reaches in any one of them and multiply: 2³ × 3² × 5 = 360.

    Can you get the LCM of 20, 24 and 45 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 20 and 24 is 120, and the LCM of 120 and 45 is 360 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 360 divisible by 20, 24 and 45?

    Yes, and by definition it is the smallest positive integer that is: 360 ÷ 20, 360 ÷ 24 and 360 ÷ 45 all come out whole. Any other common multiple of 20, 24 and 45 is a multiple of 360.

    See Also